
n this work, we provide examples of a cofrontier dynamics, where the dynamics restricted to two complemenary domains induce two (different) irrational prime ends rotation numbers. Such example is a complement of Walkers examples in 1991. In that paper, Walker made a conjecture that such example can not exist if one also requires the prime ends circle dynamics is transitive. This conjecture was proved by le Calvez, Nassiri and Koropecki in 2015.
This is a joint work with Jan Boronski and Jernej Cinc.